De Gea achieved the landmark in Sunday's 2-0 win over Newcastle United in the Carabao Cup final, surpassing the great Peter Schmeichel with his 181st shut-out.
It was Ferguson who signed a fresh-faced De Gea from Atletico Madrid in the summer of 2011 and he has also gone on to win the Premier League, Europa League and FA Cup in his time at the club.
In a video released on Manchester United's official website, Ferguson said: "David, congratulations to think all those years back then when I signed you as a young kid, you've beaten all the goalkeeping records at this football club, I just want to say well done you deserve it so enjoy the moment, thanks very much for your service to the club."
"David, in a massive career to collect a clean sheet record in this massive club it's a huge performance," said Erik Ten Hag.
"I hope to come many more clean sheets and to make this record even sharper because as you know the clean sheets are the base for winning games and for winning trophies.
"You've beaten all the goalkeeping records at this football club."
Team-mate Bruno Fernandes added: "I think everyone is really happy for you, you deserve that, you deserve to be in that position, you are a legend for the club you know that.
"Hopefully you will get more and more clean sheets in this season and for the future also because I hope we can keep you here with us for so many years."
Rio Ferdinand said: "Broke the record for clean sheets, man. Never, ever in doubt. Always backed you my guy. Keep up the good work."
